Ashley is 20 years younger than Omar. For the last 3 years, Omar and Ashley have been going to the same school. Nineteen years ago, Omar was 3 times as old as Ashley. How old is Omar now?
Solution: We can use the given information to write down two equations that describe the ages of Omar and Ashley. Let Omar's current age be $o$ and Ashley's current age be $a$ The information in the first sentence can be expressed in the following equation: $o = a + 20$ Nineteen years ago, Omar was $o - 19$ years old, and Ashley was $a - 19$ years old. The information in the second sentence can be expressed in the following equation: $o - 19 = 3(a - 19)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $o$ , it might be easiest to solve our first equation for $a$ and substitute it into our second equation. Solving our first equation for $a$ , we get: $a = o - 20$ . Substituting this into our second equation, we get the equation: $o - 19 = 3($ $(o - 20)$ $ -$ $ 19)$ which combines the information about $o$ from both of our original equations. Simplifying the right side of this equation, we get: $o - 19 = 3o - 117$ Solving for $o$ , we get: $2 o = 98$ $o = 49$.